As some might know (although I and others have to repeat this regularly…), if you enable directory synchronization from your on-premises Active Directory (AD) and you migrate all you Exchange mailboxes to Exchange Online you still require an Exchange server to manage mail(box) objects. It is the only supported solution, even though some use third party tooling or ADSIedit. Luckily this managing Exchange server doesn’t require the same amount of resources compared to Exchange serves hosting actual production mailboxes. In